## A binary powering Schur algorithm for computing primary matrix roots.(English)Zbl 1202.65053

The authors propose a new algorithm based on the Schur normal form, for computing a primary $$p$$th root of an $$n \times n$$ complex matrix. They prove that the cost of the proposed algorithm is lowered to $${\mathcal{O}}(n^2 p + n^3 \log_2 p)$$ ops and the storage is lowered to $${\mathcal{O}}(n p + n^2 \log_2 p)$$ real numbers.

### MSC:

 65F30 Other matrix algorithms (MSC2010) 15A24 Matrix equations and identities 15A16 Matrix exponential and similar functions of matrices

### Software:

mftoolbox; mctoolbox
Full Text:

### References:

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